Math Answers

For each of the ff. sets, determine whether 2 is an element of that set.

1. {{2},{2,{2}}}
2. {{{2}}}

Determine whether the distribution represents a probability distribution. Explain your answer.

X

1

3

5

7

P(X)

0.35

0.25

0.22

0.12

Find Elementary matrices E1, E2 so that E2 E1 A = I2, where A = matrix(1 0 2 3) and I2 is the respective identity matrix

In a Competitive examination of 5000 students, the marks of the examinees in statistics were found to be distributed normally with mean 45 and standard deviations 14.

Determine the number of examinees whose marks, out of 100 were;

(i) Less than 30.                                                         2MKS

(ii) Between 30 and 70.                                              2MKS

(iii) Between 60 and 80.                                          2MKS

(iv) More than 60.                                                 2MKS

(v) More than 40                              2MKS

Find the corresponding area between z = 0 and each of the following.

1. Z = 0,85

2. Z = 1.27

3. z = 2.86

4. Z = -1.05

5. Z = -2.96

Find a basis and the dimension of the subspace W of ℝ^3 where W = {( x, y, z ) ∈ ℝ^3 ∶ x + y + z = 0 }.

Express each of these mathematical statements using predicates, quantifiers, logical connectives, and mathematical operators.

a) The product of two negative real numbers is positive.

b) The difference of a real number and itself is zero.

c) Every positive real number has exactly two square roots.

d) A negative real number does not have a square root that is a real number. e) Every non-zero real number has a unique reciprocal. 

Determine the subspace of ℝ^3 spanned by the vectors α = 1, 2, 3 , β = 3, 1, 0 . Examine whether

γ = 2, 1, 3 , δ = (−1, 3, 6) are in the subspace or not.

A university has analyzed the results of 1,000 students after the first year examinations. The result of the analysis is summarized below

Types of sponsorship

Examination results

Government

Private

Church

Students who were to be discontinued

155

150

105

Students who passed the examination

180

195

170

Students who were to sit for a supplementary paper

20

5

20

Required

The probability that a student was discontinued or was required to sit for a supplementary paper                                                                         (1mark)

The probability that a student was a government sponsored           (1mark)

The probability that a privately sponsored student passed the examination                                                                                                           (2marks)